Design: Blocked Cluster RCT, with 3 levels, and randomization done at level 2 (school level).

Models: random and fixed treatment effects.

Default parameters:

  • M = 3
  • J = 20
  • K = 10
  • rho: \(\rho\) = 0.5
  • ATE ES = 0.125, 0.125, 0.125
  • R21, R22: \(R^2_1\) = 0.1, 0.1, 0.1, \(R^2_2\) = 0.1, 0.1, 0.1
  • ICC2: \(\text{ICC}_2\) = 0.2, 0.2, 0.2
  • Omega: \(\omega_2\) = 0, \(\omega_3\) = 0.1

Parameters by model type:

  • R23: \(R^2_3 = 0\) for fixed effects model, \(R^2_3\) = 0.1, 0.1, 0.1 for random effects model
  • ICC3: \(\text{ICC}_3 = 0\) for fixed model, \(\text{ICC}_3\) = 0.2, 0.2, 0.2 for random effects model

Power Validation

Varying school size

\(\bar{n}\) = 100

\(\bar{n}\) = 75

\(\bar{n}\) = 50

Varying R2

\(R^2_1 =\) 0.6, 0.6, 0.6

\(R^2_2 =\) 0.6, 0.6, 0.6

\(R^2_3 =\) 0.6, 0.6, 0.6

\(R^2_1 =\) 0, 0, 0 \(R^2_2 =\) 0, 0, 0 \(R^2_3 =\) 0, 0, 0

Varying rho

\(\rho =\) 0.2

\(\rho =\) 0.8

Varying true positives

ATE (ES) = 0.125, 0, 0

Varying ICC

\(\text{ICC}_2\) = 0.7, 0.7, 0.7

\(\text{ICC}_3\) = 0.7, 0.7, 0.7

Varying Omega

\(\omega_3\) = 0.8

\(\omega_3\) = 0.8 \(\text{ICC}_3\) = 0.7, 0.7, 0.7

MDES validation

## 
## 
## +------------+---------------+---------------+-------------+
## |    MTP     | Adjusted MDES | D1indiv Power | Target MDES |
## +============+===============+===============+=============+
## |    rawp    |     0.126     |     0.517     |    0.125    |
## +------------+---------------+---------------+-------------+
## | Bonferroni |     0.125     |     0.34      |    0.125    |
## +------------+---------------+---------------+-------------+
## |     BH     |     0.127     |     0.447     |    0.125    |
## +------------+---------------+---------------+-------------+
## |    Holm    |     0.125     |     0.398     |    0.125    |
## +------------+---------------+---------------+-------------+
## 
## Table: blocked_c2_3f
## 
## 
## +------------+---------------+---------------+-------------+
## |    MTP     | Adjusted MDES | D1indiv Power | Target MDES |
## +============+===============+===============+=============+
## |    rawp    |     0.125     |     0.261     |    0.125    |
## +------------+---------------+---------------+-------------+
## | Bonferroni |     0.125     |     0.104     |    0.125    |
## +------------+---------------+---------------+-------------+
## |     BH     |     0.124     |     0.161     |    0.125    |
## +------------+---------------+---------------+-------------+
## |    Holm    |     0.129     |     0.139     |    0.125    |
## +------------+---------------+---------------+-------------+
## 
## Table: blocked_c2_3r

Sample size validation

## 
## 
## +------+-------------+-------------+---------------+--------------------+
## | MTP  | Sample type | Sample size | D1indiv power | Target sample size |
## +======+=============+=============+===============+====================+
## |  BH  |      K      |     11      |     0.441     |         10         |
## +------+-------------+-------------+---------------+--------------------+
## | Holm |      K      |     10      |     0.386     |         10         |
## +------+-------------+-------------+---------------+--------------------+
## 
## Table: blocked_c2_3f
## 
## 
## +------+-------------+-------------+---------------+--------------------+
## | MTP  | Sample type | Sample size | D1indiv power | Target sample size |
## +======+=============+=============+===============+====================+
## |  BH  |      K      |     10      |     0.168     |         10         |
## +------+-------------+-------------+---------------+--------------------+
## | Holm |      K      |     10      |     0.125     |         10         |
## +------+-------------+-------------+---------------+--------------------+
## 
## Table: blocked_c2_3r